Solve for $x$ and $y$ using elimination. $\begin{align*}4x+6y &= 3 \\ -2x+2y &= 4\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $1$ and the bottom equation by $2$ $\begin{align*}4x+6y &= 3\\ -4x+4y &= 8\end{align*}$ Add the top and bottom equations. $10y = 11$ Divide both sides by $10$ and reduce as necessary. $y = \dfrac{11}{10}$ Substitute $\dfrac{11}{10}$ for $y$ in the top equation. $4x+6( \dfrac{11}{10}) = 3$ $4x+\dfrac{33}{5} = 3$ $4x = -\dfrac{18}{5}$ $x = -\dfrac{9}{10}$ The solution is $\enspace x = -\dfrac{9}{10}, \enspace y = \dfrac{11}{10}$.